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Finding the k Shortest Paths
, 1997
"... We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest pat ..."
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Cited by 401 (2 self)
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We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest
Construction of minimumweight spanners
 In Proc. of the 12th European Symposium on Algorithms
, 2004
"... Abstract. Spanners are sparse subgraphs that preserve distances up to a given factor in the underlying graph. Recently spanners have found important practical applications in metric space searching andmessage distribution in networks. These applications use some variant of the socalled greedy algori ..."
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Cited by 2 (0 self)
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algorithm for constructing the spanner — an algorithm that mimics Kruskal’s minimum spanning tree algorithm. Greedy spanners have nice theoretical properties, but their practical performance with respect to total weight is unknown. In this paper we give an exact algorithm for constructing minimumweight
Planar MinimumWeight Triangulations
, 1995
"... The classic problem of finding a minimumweight triangulation for a given planar straightline graph is considered in this paper. A brief overview of known methods is given in addition to some new results. A parallel greedy triangulation algorithm is presented along with experimental data that sugge ..."
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Cited by 2 (0 self)
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The classic problem of finding a minimumweight triangulation for a given planar straightline graph is considered in this paper. A brief overview of known methods is given in addition to some new results. A parallel greedy triangulation algorithm is presented along with experimental data
Finding community structure in networks using the eigenvectors of matrices
, 2006
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible div ..."
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Cited by 500 (0 self)
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We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of realworld complex networks.
An Efficient Algorithm for MinimumWeight Bibranching
 JOURNAL OF COMBINATORIAL THEORY
, 1996
"... Given a directed graph D = (V; A) and a set S ` V , a bibranching is a set of arcs B ` A that contains a v(V n S) path for every v 2 S and an Sv path for every v 2 V n S. In this paper, we describe a primaldual algorithm that determines a minimum weight bibranching in a weighted digraph. It ..."
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Cited by 7 (1 self)
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Given a directed graph D = (V; A) and a set S ` V , a bibranching is a set of arcs B ` A that contains a v(V n S) path for every v 2 S and an Sv path for every v 2 V n S. In this paper, we describe a primaldual algorithm that determines a minimum weight bibranching in a weighted digraph
Minimumweight Cycle Covers and Their Approximability
, 2008
"... A cycle cover of a graph is a set of cycles such that every vertex is part of exactly one cycle. An Lcycle cover is a cycle cover in which the length of every cycle is in the set L ⊆ N. We investigate how well Lcycle covers of minimum weight can be approximated. For undirected graphs, we devise no ..."
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Cited by 1 (0 self)
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A cycle cover of a graph is a set of cycles such that every vertex is part of exactly one cycle. An Lcycle cover is a cycle cover in which the length of every cycle is in the set L ⊆ N. We investigate how well Lcycle covers of minimum weight can be approximated. For undirected graphs, we devise
Approximability of Minimumweight Cycle Covers
, 2006
"... A cycle cover of a graph is a set of cycles such that every vertex is part of exactly one cycle. An Lcycle cover is a cycle cover in which the length of every cycle is in the set L ⊆ N. For most sets L, computing Lcycle covers of minimum weight is NPhard and APXhard. While computing Lcycle cove ..."
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A cycle cover of a graph is a set of cycles such that every vertex is part of exactly one cycle. An Lcycle cover is a cycle cover in which the length of every cycle is in the set L ⊆ N. For most sets L, computing Lcycle covers of minimum weight is NPhard and APXhard. While computing L
Theoretical improvements in algorithmic efficiency for network flow problems

, 1972
"... This paper presents new algorithms for the maximum flow problem, the Hitchcock transportation problem, and the general minimumcost flow problem. Upper bounds on ... the numbers of steps in these algorithms are derived, and are shown to compale favorably with upper bounds on the numbers of steps req ..."
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Cited by 565 (0 self)
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are given. We show that, if each flow augmentation is made along an augmenting path having a minimum number of arcs, then a maximum flow in an nnode network will be obtained after no more than ~(n a n) augmentations; and then we show that if each flow change is chosen to produce a maximum increase
Results 1  10
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1,477,404